$\begin{array}{llll} & L & C & R \\ U & 1 ; 10 & -1 ; 4 & 5 ; 5 \\ M & 4 ;-1 & 0 ; 0 & 4 ;-5 \\ D & 10 ; 10 & -4 ; 5 & 10 ; 5\end{array}$
If this game is played infinite times with a discount rate=alpha and if strategies are like this; ((U,R) if t=1 or (U,R) was played before) ((M,C) else.) Then how can I prove that if "alpha" is high enough than this is the SPE of infinitely repeated game and how can I find the minimal "alpha" so that it is an equilibrium? I know the basics of finitely repeated game but this is impossible for me to solve.